A new level set method for systematic design of hinge-free compliant mechanisms

This paper presents a new level set-based method to realize shape and topology optimization of hinge-free compliant mechanisms. A quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is employed to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. The design of compliant mechanisms is mathematically represented as a general non-linear programming with a new objective function augmented by the high-order energy term. The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. In doing so, it is expected that numerical difficulties such as the Courant-Friedrichs-Lewy (CFL) condition and periodically applied re-initialization procedures in most conventional level set methods can be eliminated. In addition, new holes can be created inside the design domain. The final mechanism configurations consist of strip-like members suitable for generating distributed compliance, and solving the de-facto hinge problem in the design of compliant mechanisms. Two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms.